The magnitude of the errors in the visual assessment of colour differences is discussed. The errors are likely to vary with the particular form of visual assessment. Methods are described for estimating visual errors from data in which the visual assessments are expressed as percentage acceptance and rank orders as well as ratios of other colour differences. The results indicate that experienced observers tend to have a greater degree of discrimination than inexperienced observers. Between‐observer variation is greater than within‐observer variation, suggesting that the mean of many repeat observations by a single observer may differ significantly from the mean derived from a number of different observers. For colour passing, the error of a single observer varies with the size of the colour difference and is given by the equation: σ=0.4+ 0.25 δν where δν is the true visual difference expressed in units equivalent to the average unit given by the AN40 equation.
Methods of describing the extent of agreement between the ΔE values calculated from a colour‐difference equation and the corresponding visual estimates of colour difference are discussed. Lack of agreement will be due to a combination of errors in the visual assessments, in the measurements, and in the colour‐difference equation itself. If there were no error in the instrumental measurements, the equation error for a particular colour difference would be the difference between the calculated ΔE value and the mean visual assessment of a very large number of observers (ΔVtrue). Experimental data in the form of acceptances (%) can be converted to ΔV values directly proportional to the observed colour differences. The overall equation error for n colour differences can be calculated from Eqn 1. The Davidson and Friede data are considered to be the most satisfactory of those presently available for testing the suitability of equations for industrial colour‐tolerance work and have been used to assess the accuracy of several well‐known equations. After allowing for errors in the visual assessment and in the instrumental measurements, σ(log ΔE) for the 1964 CIE equation was 0.22. Similar values (0.16‐0.23) were found for other equations. A lower a‐value was found for a very simple empirical equation essentially based on the x, y chromaticity diagram rather than on any transformation of it. The usual transformations tend to be based on data covering the whole chromaticity gamut, whereas real surface colours cover only a fraction of the possible area. This fact, together with the knowledge that most equations are based on data corresponding to small fields of view or large colour differences, could account for the relative failure of the standard equations.
A set of gloss‐paint samples exhibiting large (10–25 CIE units) colour differences has been prepared. Visual assessments have been made under different viewing conditions. The results substantiate the view that visual assessments vary markedly with the size of sample and, together with earlier work (2), show that assessments also vary with the size of the colour difference. Thus, colour‐difference equations can correlate well with visual assessments only for given conditions. Existing equations apply best to conditions very different from those encountered in industry. It should not be too difficult to develop a more suitable equation for industrial use, given sufficient experimental data obtained under appropriate viewing conditions.
A new series of green paint samples has been prepared and used to study different methods of obtaining visual assessments of colour differences and of scaling the experimental results to give Δ V values directly proportional to the observed differences. The results from two standard methods (the ratio method and the paired‐comparison method) were in good agreement with each other and with results from the ranking method used earlier, thus adding confidence to conclusions based on the use of the latter method. The extent of agreement between ΔE values calculated from some best‐fit empirical colour‐difference equations and the ΔV values has been calculated. Results obtained by Robinson on a series of blue‐grey paint samples by a % acceptance method have been re‐analysed. The scaling method used previously with visual results in the form of % acceptance values gives ΔV values directly proportional to calculated ΔE values. The visual observers can be subdivided into two groups based on whether they had experience of colour matching or not. No evidence was found for any difference between the ‘perceptibility’ and ‘acceptability’ of colour differences in the sense that different colour‐difference equations might have been required to represent the two groups of observers.
Presented at a symposium jointly organised by the West Riding Region and Wira, held at Wira, Leeds, on 16 February I9 72 The quantitative data available for expressing the errors associated with visual assessments, measurements and colour-difference equations have been used to calculate, for given sets of circumstances, the pass and rejection rates at various stages from the dyer to the retailer to the final customer. The main errors arise in the visual assessments and the colour-difference equations and, for the average of the available equations, these two errors are roughly comparable in magnitude, They do, however, vary with size of colour difference in different ways such that for small differences (0-1 AN40 units) the equations agree better with the true colour differences than a single visual assessment, whereas the reverse is true for large differences (above 2 AN40 units). Detailed results depend on the distribution of samples over the range of colour differences considered, together with the sizes of colour-tolerance limits set. Two initial distributions for the dyer have been assumed, one with same number of samples at all colour differences and the other simulating the distribution used in the Davidson and Friede study. For each, the results of use of a 'low tolerance'(0.S AN40 unit) and a 'high tolerance' (1.S AN40 units) by the dyer have been calculated. At low tolerance, the average equation provides much greater satisfaction than one assessor and improved equations will not give much more satisfaction. A t high tolerance, the average equation could give greater or less satisfaction depending on the precision of the particular assessor and the exact distribution of samples to be considered, but there are considerable benefits to be gained by improvement in equation performance. Some of the likely interactions between the dyer and his customers are illustrated, showing that difficulties could arise unless there is some degree of co-operation. This is particularly true if unilateral action for equation use is taken by the retailer working to his customary tolerance limit. It would appear that the introduction of the use of an equation should first be made by the dyer, but if made by the retailer then consultation with the dyer is essential, The use of an equation by a retailer provides little benefit except in reducing dyer-retailer disputes. (MS.
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